I wanted to leave this as a comment but it's running long.
I ultimately decided not to go to see the sunrise. It seems the best option for doing so is to stay overnight on or near the wall (perhaps staying at Mu'tian'yu Great Wall [暮田峪长城]).
A few tidbits of further advice that I picked up in the process of coming to this decision:
My initial enthusiasm for Jian'kou [箭扣] was fuelled by finding it here on Baidu maps. From what I can tell, however, this is incorrect. I'm not positive if one could reach Jian'kou from there; anyway, it might take someone from that area's level of know-how to navigate that trek in pitch black (even if you do know Chinese, it seems you shouldn't expect to find many, if any, people out and about in the mountains at 3 AM to point you in the right direction; more below).
You can see from a search for a map of Jian'kou that all the maps seem to point to the same basic setup:
Jian'kou is situated between the Wo'fo mountain resort (not sure the Chinese for this) and the Xi'zha'zi [西栅子] villages (e.g., here, from what I can tell). It seems Google Maps has a better idea of where it is, but relying on this means relying on VPN.
- Some external reading I found useful: 1, 2, 3 (I believe 2&3 are behind the Firewall). Basically, the consensus seems to be that if you want to do this, you should arrive to Xi'zha'zi villages, make a donation to some locals, then make your way to Zheng'bei'lou [正北楼].
But therein lies the hitch with my original plan. Basically, to get a taxi to Xi'zha'zi is doable -- roughly the same price as to "Jian'kou".
But, it takes about two hours. And if you really want to see sunrise from the Great Wall (as opposed to seeing it while in the woods near the Great Wall), I estimated I'd need at least an extra two hours upon arrival to situate myself and to navigate in the dark.
All told, then, to make a 5 AM sunrise would require heading to Xi'zha'zi at 1 AM, at the latest.
So you're in for an all-nighter.
This is still a viable plan, but perhaps not so wise (why not just pay to stay near Mu'tian'yu? probably comparable to downtown Beijing anyway), and would have torched my sleep schedule for some time.
Best of luck to anyone else brave enough to try this! Perhaps it'll make more sense to do so in the Fall/early Spring when the sunrise isn't so early.